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Based on the nonincreasing property of quantum coherence via skew informationunder incoherent completely positive and trace-preserving maps, we propose anon-Markovianity measure for open quantum processes. As applications, byapplying the proposed measure to some typical noisy channels, we find that itis equivalent to the three previous measures of non-Markovianity for phasedamping and amplitude damping channels, i.e., the measures based on the quantumtrace distance, dynamical divisibility, and quantum mutual information. For therandom unitary channel, it is equivalent to the non-Markovianity measure basedon $l_1$ norm of coherence for a class of output states and it is incompletelyequivalent to the measure based on dynamical divisibility. We also use themodified Tsallis relative $\alpha$ entropy of coherence to detect thenon-Markovianity of dynamics of quantum open systems, the results show that themodified Tsallis relative $\alpha$ entropy of coherence are more comfortablethan the original Tsallis relative $\alpha$ entropy of coherence for small$\alpha$.

Quantifying quantum non-Markovianity based on quantum coherence via skew information